Equations - August 2007, All Stages

Problems

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Number Lines

Stage: 1 Challenge Level: Challenge Level:1

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

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Secret Number

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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Getting the Balance

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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Shape Times Shape

Stage: 2 Challenge Level: Challenge Level:1

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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Balance of Halves

Stage: 2 Challenge Level: Challenge Level:1

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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Two Number Lines

Stage: 2 Challenge Level: Challenge Level:1

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

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Parallel Lines

Stage: 3 Challenge Level: Challenge Level:1

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

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Clocking Off

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

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Temperature

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

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Perpendicular Lines

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

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Matchless

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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Gutter

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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Reasonable Algebra

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

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Equation Attack

Stage: 5 Challenge Level: Challenge Level:1

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

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Production Equation

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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Resistance

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the equation from which to calculate the resistance of an infinite network of resistances.